Hurricane Final Report
Yuanming Leng, Biyao Zhang, Chen Xu, Xihao Cao
11/20/2021
## [using ordinary kriging]## [using ordinary kriging]
## [using ordinary kriging]Movement Track
Hurricane Ike was a powerful tropical hurricane that swept through portions of the Greater Antilles and Northern America in September 2008. The origins of Hurricane Ike can be traced back to a well-defined tropical wave first identified by the National Hurricane Center (NHC) near the western coast of Africa on August 28. After a period of development, Ike made its first landfall on Inagua in the Bahamas at 13:00 UTC on September 7 with winds of 125 mph (201 km/h). After one day, Ike made its second landfall on Cuba with a Category 4 intensity. Then, at 0700 UTC on September 13, Ike made its third landfall on Galveston Island in Texas (N29.4, W-95.01), with a Category 2 intensity and a maximum wind speed of 110 mph (180 km/h). Then Ike moved northward after its landfall on Texas and weakened to a tropical storm status.
Loss and Damage:
Ike is the seventh-costliest hurricane in United States history until now, it caused over $38 billion damage and 214 casualties. And due to the intensity of the storm, Texas closed many of its chemical plants and oil refineries which caused many indirect economy losses in the mean time.
Buoys selected
Our project will only focus on the conditions of Ike when it made its landfall in Texas. We selected 8 Buoys from the NOAA database to analyze Ike. All 8 buoys are located near the center of the landfall location, the maximum distance between two buoys is around 60 miles, and the minimum distance is around 25 miles. The selected Buoys IDs are: GRRT2(29.302 N 94.896 W), 42043(28.982 N 94.899 W), GNJT2(29.357 N 94.725 W), 42035(29.232 N 94.413 W), EPTT2(29.481 N 94.917 W), MGPT2(29.682 N 94.985 W), CLLT2(29.563 N 95.067 W), RLOT2(29.515 N 94.513 W).
EDA of Buoys data
Firstly we use the buoys data to get the gust wind speed vs time and wind speed vs time. Notice that the timeline is from 6:00 on 2008-09-11 to 18:00 on 2008-09-15 which contains the time Ike made its landfall(September 13th). Each line represents the wind speed variation at one specific buoy, and there are 8 buoys, thus 8 lines in total. As we can see, the 8 lines share the same overall shape in both graphs, where the wind speeds reaches their maximum around 6:00 on 2008/9/13 which is very close to the landfall time of Ike(7:00 UTC). Meanwhile, we can see that the wind speeds decrease under 10m/s after 6:00 on 2008/9/14, which was also close to the time Ike left the landfall neighborhood. If we compare the information of Ike in the Hurricane Exposure with these graphs, we can see that they share almost the same timeline, which is what we want.
Secondly, we use the buoys data to get the sea level pressure vs. time time series plot. Notice that the timeline is from 6:00 on 2008-09-11 to 18:00 on 2008-09-15 which contains the time Ike made its landfall(September 13th at 7:00AM). Each line represents the sea level pressure(hPa) at one specific buoy, and there are 5 buoys recorded the data, thus 5 lines in total.
Sea level pressure – the same metric that we all use to guess if the weather is getting better or worse by seeing if the pressure is rising or falling – is already a common test of strength used in hurricanes and storm systems around the globe.
Generally, the lower the central pressure, the stronger the storm. The lowest pressure in a hurricane is always found at its center, or in its eye.
We can see from the plot that the sea level pressure recorded by buoy reaches to its lowest level around September 13th at 7:00AM, when Ike landfall. Hurricane Ike was a Category 2 on the Saffir–Simpson hurricane wind scale (SSHWS) but had a pressure of around 950 hPa when it arrived on the Texas coast. This was the third-lowest pressure for a landfalling Category 2 since 1900. Ike caused about $38 billion in damage, according to the National Hurricane Center. In 2009, Ike ranked as the second-costliest hurricane to make landfall in the United States. Since then, more damaging storms have made landfall, but Ike remains as the sixth-most-damaging hurricane. As we can conclude that sea level pressure may be another useful indicator of Hurricane Damage Potential besides wind speed and rainfall. 
EDA of Hurricane_Package data
The following four graphs illustrate the data of Ike in the Hurricane package.
This graph shows the wind speed variation of Ike along its tract. As we can see that the maximum speed Ike reached in the U.S. is around 45m/s at the landfall area, which is consistent with the peak value of our wind speed graph above. 
The second graph we have is the map of tornados event that were caused by Ike. Although tornado is another another topic, we can get some useful information from its distribution. Notice that most of the exposed area also encountered higher amount of rainfall, but we could not find a clear relationship between the wind speed of Ike and the tornado events. 
The third figure here is flood event exposed when Ike transits with Ike’s track and the fourth figure is the rainfall map when Ike transit in 2008. In addition to high winds, hurricanes threaten coastal areas with their heavy rains. All tropical cyclones can produce widespread torrential rains, which cause massive flooding and trigger landslides and debris flows. Flash flooding, a rapid rise in water levels, can occur quickly due to intense rainfall over a relatively short period of time. As we can see from these two figures, the area has major rainfall and the area where flood events occur are overlap. 
Variogram
Plots show the semivariogram values as a function of sample point separation h. In the case of empirical semivariogram, separation distance bins are used rahter than exact distances, and usually isotropic comditios are assumed. Then, the empirical semivariogram can be calculated for each bin: \[ \hat{\gamma}(h \pm \delta):=\frac{1}{2|N(h \pm \delta)|} \sum_{(i, j) \in N(h \pm \delta)}\left|z_{i}-z_{j}\right|^{2} \]
We choose Gaussian variogram model: \[ \gamma(h)=(s-n)\left(1-\exp \left(-\frac{h^{2}}{r^{2} a}\right)\right)+n 1_{(0, \infty)}(h) \]
Using data from hurricane exposure data package:
For upper plot, the y axis is the semi-variance of wind speed of Ike near the landfall point, and the x axis is the distance between two spacial points pair. The second graph has the same axis but illustrates the spatial points into four directions.
#### Wind speed along track prediction using kriging:
The first one is a heatmep while the second graph has each point being a county with the united states map as the background. Both graphs use the krigging to smooth the original data from the hurricane package, and they both show the overall track of Ike.
Rainfall along track:
The picture shows the experimental variogram and fitted model for rainfall. The variogram of rainfall showed a clear spatial dependence with bounded sill and were fitted well with Gaussian models.
We detect anisotropy by visualization by the variogram map and directional variograms. Anisotropy is the property of a material which allows it to change or assume different properties in different directions as opposed to isotropy.
The dynamic map shows the rainfall distribution of hurricane exposure data package. It is obvious that there is more rainfall in coastal areas, so rainfall in coastal areas is more affected by hurricanes IKE.